Master’s Thesis
Feasibility study of short-lived neutral K
meson measurement in Au + Au collisions√
at sN N = 200 GeV at PHENIX
Masaya Nihashi(M086916)
Department of Physics
Hiroshima University Graduate School

Supervisor : Prof. Toru Sugitate
Primary examiner : Associate Prof. Kenta Shigaki
Examiner : Prof. Yasushi Fukazawa
February 10, 2010

Contents
1 Introduction
1.1 Historical introduction . . . . . . . . . . . . . . . . . . . . . .
1.2 High energy heavy ion collision . . . . . . . . . . . . . . . . .
1.2.1 The picture of heavy ion collisions . . . . . . . . . . . .
1.2.2 Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.3 Nuclear modification factor . . . . . . . . . . . . . . .
1.2.4 Jet conversion . . . . . . . . . . . . . . . . . . . . . . .

1
1
3
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5
5

2 Experimental setup
2.1 The RHIC accelerator . . . . . . . . . . . . . . . . . . . . . .
2.2 The PHENIX detectors . . . . . . . . . . . . . . . . . . . . . .
2.2.1 PHENIX complex overview . . . . . . . . . . . . . . .
2.2.2 Zero Degree Calorimeter(ZDC) . . . . . . . . . . . . .
2.2.3 Beam Beam Counter(BBC) . . . . . . . . . . . . . . .
2.2.4 Electro-Magnetic Calorimeter(EMCal) . . . . . . . . .
2.2.5 Data acquisition system(DAQ) . . . . . . . . . . . . .

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3 Analysis
3.1 Analysis Method . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Single simulations . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Event Generator . . . . . . . . . . . . . . . . . . . . .
3.2.2 Detector Simulation . . . . . . . . . . . . . . . . . . .
3.2.3 Comparison between the landau fitting and gaussian
fitting for 4 photons invariant mass distribution . . . .
3.2.4 Estimation of the Decay Vertex Location . . . . . . . .
3.3 Embedding simulation . . . . . . . . . . . . . . . . . . . . . .

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4 Results and Discussion
4.1 Comparison between DVL analysis and normal analysis . . . .
4.1.1 Results of DVL analysis for π 0 s from K 0 S . . . . . . .
4.1.2 Results of DVL analysis for K 0 S . . . . . . . . . . . . .
4.2 Multiplicity effects . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 The results of the multiplicity effects for π 0 s from K 0 S
4.2.2 The results of the multiplicity effects for the K 0 S measurement . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5 Conclusion

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List of Figures
1.1

1.2
1.3
1.4
1.5

1.6
2.1
2.2
2.3
2.4
2.5
2.6

2.7
2.8
2.9

Lattice QCD[3] results for the energy density/T 4 as a function of the temperature scaled by the critical temperature TC .
Note the arrows on the right side indicating the values for the
Stefan.Boltzmann limit. . . . . . . . . . . . . . . . . . . . . . 2
Schematic view of two colliding nuclei in the geometical participantspectator model[15]. . . . . . . . . . . . . . . . . . . . . . . . 3
Exaggerated polt of observed rapidity distribution of generated hadrons in ultra-reativistic nuclei collisions . . . . . . . . 4
K±and p(p̄)
ratios in jets with energies Ejet = 50, 100and200GeVπ±π±[4]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
K0s spectra from quark and gluon jet fragmentation in p+p√
collisions at sN N = 200GeV [8]. Data are from STAR Collaboration[9].
RAA for K 0 S in Au + Au collisions at same center mass energy
as a function of transverse momentum [11]. . . . . . . . . . . . 9√
RAA for K 0 S in P b + P b collisions at sN N = 5.5T eV asfunction of transverse momentum[11]. . . . . . . . . . . . . . . 9
Schematic view of the RHIC complex[16]. . . . . . . . . . . . . 11
The PHENIX Detector configuration(2007)[17]. . . . . . . . . 12
The configuration and the location of Zero Degree Calorimeter(ZDC)[18]. 13
One element of Beam Beam Counter(BBC)[19]. . . . . . . . . 14
The location of Beam Beam Counters north and south(BBC)[19]. 15(left)Interior view of one PbSc tower, consisting of 66 layers,
this show only 3 layers (right)Interior view of one PbSc module, consisting of four towers[20]. . . . . . . . . . . . . . . . . 16
A PbGl tower and image of one supermodule[20]. . . . . . . . 17
Image of a cluster. . . . . . . . . . . . . . . . . . . . . . . . . 18
Block diagram of the PHENIX Online System[21]. . . . . . . . 20

3

Image of the 2 π 0 decay mode of K 0 S hitting to the EMCal.
K 0 S decay into 2 π 0 and each π 0 decay into 2 γ. . . . . . . .
3.2 Schematic view of a single K 0 S event in the real event, here
θ12 is the true opening angle between γ1 and γ2 , and θ34 is thetrue opening angle between γ2 and γ4 . . . . . . . . . . . . . .
3.3 Schematic view of a single Ks0 event on calculation, here θ0 12
is the calculated opening angle between γ1 and γ2 , and θ0 34 is
the calculated opening angle between γ2 and γ4 . . . . . . . .
3.4 Diagram of the cluster merging and the cluster spliting on acluster algorithm. . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 The pT distribution of primary K 0 S . . . . . . . . . . . . . . .
3.6 Invariant mass spectrum of single K 0 S events for high pT witha gaussian fitting. . . . . . . . . . . . . . . . . . . . . . . . . .
3.7 Invariant mass spectrum of single K 0 S events for high pT witha landau fitting. . . . . . . . . . . . . . . . . . . . . . . . . . .
0
3.8 four gamma invariant mass distribution in 4.5GeV ≤ pT K S ≤5GeV with a gaussian fit. . . . . . . . . . . . . . . . . . . . . .
0
3.9 four photons invariant mass distribution in 11.5GeV ≤ pT K S≤ 12GeV with a gaussian fit. . . . . . . . . . . . . . . . . . .
3.10 Peak position of the K 0 S as a function of the pT with thelandau and gaussian fitting. . . . . . . . . . . . . . . . . . . .
3.11 Peak width of the K 0 S as a function of the pT with the landau
and gaussian fitting. . . . . . . . . . . . . . . . . . . . . . . .
3.12 Chi square of the landau and gaussian fitting about the mass
peak of the K 0 S . . . . . . . . . . . . . . . . . . . . . . . . . .
3.13 Image of Decay Vertex Location(DVL). . . . . . . . . . . . . .
3.14 Invariant mass peak of 2 photons with gaussian fitting. The
red line is to take into account the DVL. The green line is not
to take into account the DVL. . . . . . . . . . . . . . . . . . .
3.15 The width of the 2 photons invariant mass with gaussian fitting. The red line is to take into account the DVL. The green
line is not to take into account the DVL. . . . . . . . . . . . .
3.16 Peak of the 4 photons invariant mass with landau fitting. The
red line is to take into account the DVL. The green line is not
to take into account the DVL. . . . . . . . . . . . . . . . . . .
3.17 Width of the 4 photons invariant mass with landau fitting.
The red line is to take into account the DVL. The green line
is not to take into account the DVL. . . . . . . . . . . . . . .

3.1

4

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27
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3.18 χ2 of a landau fitting. The red line is to take into account the
DVL. The green line is not to take into account the DVL. . . .
3.19 Main flow of the embedding algorithm[15]. . . . . . . . . . . .
3.20 The invariant mass of two photons in the range of two photons
pT from 8GeV to 8.5GeV at the Minimum Bias. . . . . . . . .
3.21 The invariant mass of two photons in the range of two photons
pT from 8GeV to 8.5GeV at the peripheral collisions. . . . . .
3.22 The invariant mass of two photons in the range of two photons
pT from 8GeV to 8.5GeV at the mid central collisions. . . . .
3.23 The invariant mass of two photons in the range of two photons
pT from 8GeV to 8.5GeV at the most central collisions. . . . .
3.24 Peak position of the π 0 for the comparison between a Embedding simulation and a Single simulation. . . . . . . . . . . . .
3.25 Peak width of the π 0 for the comparison between a Embedding
simulation and a Single simulation. . . . . . . . . . . . . . . .
3.26 Chi square of the gaussian fitting about the mass peak of theπ 0 for the comparison between a Embedding simulation and aSingle simulation. . . . . . . . . . . . . . . . . . . . . . . . . .
3.27 Peak position of the π 0 for the comparison between a Embedding simulation and a Single simulation. . . . . . . . . . . . .
3.28 Peak width of the π 0 for the comparison between a Embedding
simulation and a Single simulation. . . . . . . . . . . . . . . .
3.29 Chi square of the gaussian fitting about the mass peak of theπ 0 for the comparison between a Embedding simulation and aSingle simulation. . . . . . . . . . . . . . . . . . . . . . . . . .
3.30 Peak position of the K 0 S for the comparison between a Embedding simulation and a Single simulation. . . . . . . . . . .
3.31 Peak width of the K 0 S for the comparison between a Embedding simulation and a Single simulation. . . . . . . . . . . . .
3.32 Chi square of the gaussian fitting about the mass peak of theK 0 S for the comparison between a Embedding simulation anda Single simulation. . . . . . . . . . . . . . . . . . . . . . . . .

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A ratio of π 0 peak from K 0 S between DVL analysis and normal
analysis as a 2 photons transverse momemtum(pT ). . . . . . . 47
4.2 A ratio of π 0 width from K 0 S between DVL analysis and normal analysis as a 2 photons transverse momemtum(pT ). . . . . 47

4.1

5

4.3
4.4
4.5

4.6
4.7

4.8

4.9
5.1
5.2
5.3

A ratio of K 0 S peak between DVL analysis and normal analysis as a 4 photons transverse momemtum(pT ). . . . . . . . . 48
A ratio of K 0 S peak between DVL analysis and normal analysis as a 4 photons transverse momemtum(pT ). . . . . . . . . 49
Ratio of postion of π 0 peak between embedding simulationand single simulation as a function of 2 photons pT for eachcentrality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Ratio of Width of π 0 mass between embedding simulation andsingle simulation as a function of 2 photons pT for each centrality. 51
Ratio of postion of K 0 S peak between embedding simulationand single simulation as a function of 4 photons pT for eachcentrality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Ratio of width of K 0 S peak between embedding simulationand single simulation as a function of 4 photons pT for eachcentrality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
On going PHENIX integrated luminosity as a function of weeks
into this-year-run[23]. . . . . . . . . . . . . . . . . . . . . . . . 54
The PHENIX coordinate system[17]. . . . . . . . . . . . . . . 59
landau distribution. . . . . . . . . . . . . . . . . . . . . . . . . 61
landau distribution with log scale. . . . . . . . . . . . . . . . . 61

6

Abstract
Our final goal is to qualitatively and quantitatively study of the theQuark-Gluon-Plasma(QGP), such a matter is expected to be that quarks
and gluons are no longer confined into hadrons. Quantum ChromoDynamics(QCD) predicts the QGP phase to have the number of quarks and gluons
as the degree-of-freedom at high temperatures over 170 MeV (about 2 trillions K) 1 . This phase is considered to exist in the early universe where welive few dozens micro second after Big-Bang.
The Relativistic Heavy Ion Collider(RHIC) at Brookhaven National Laboratory enables us to make a variety of measurements of the QCD multi-bodysystem with high-energy proton + proton, deutron + Au, Cu + Cu and Au+ Au collisions. These are important steps toward the understanding of theequation of state of the medium created in high-energy nuclear collisions.
Measuring an interaction between scattering partons and the QGP is aeffective way to understand properties of QGP. We detect scattering partonsas the high transverse-momentum(pT ) particles, larger than a few GeV. If
there is an interaction between scattering partons and QCD matter, scattering partons lose their energy by emitting or by emissions of gluons. As aresult, high pT particle yeild should be suppressed. We can gain the quantitative understanding of this suppression effect to measure RAA ; the suppression
ratio of particle yield in Au + Au collisions for it in proton + proton collisions. We have gotten evidences of the formed QGP by measuring RAA ofhigh pT hadrons at RHIC 2 .
My objective is a study of the phenomenon of strange quarks in the QGP
with the measurement of RAA of short-lived neutral K meson(K 0 S ) via 2
π 0 decay mode, the measurement of the RAA means to clarify the energy
loss of fast strange quarks and the presence or absence of the jet-conversion
which is the processes that jets couple to chemical properties of the QGP bycomparison of neutral π meson which is consisting of up and down quark.
In this thesis, I study how K 0 S signals look like in Au + Au collisions√
at sN N = 200GeV at PHENIX before the measurement of RAA of K 0 S .
Specifically, I estimate the multiplicity effects and the life time effect in order
to measure the peak in the invariant mass distribution with four photons from1
2

F. Karsch Lecture Notes in Physics, Vol. 583, p. 209 (2002).
J. Adams et al. (STAR Collaboration), Phy. Rev. Lett. 91, 072304 (2003)

K 0 S . High particle multiplicity generates huge backgrounds and no wonder
those backgrounds interfere cluster algorithm. In addition, the mean life
time of K 0 S which is about 0.8953 × 10−10 second 3 causes the mass shiftaccording to the pT of K 0 S and their specific life times. So I emphasize thisfeasibilty study using both simulation and real data to search the quantitative
multiplicity effects and the life time effect. Finally, I report the quantitative
multiplicity effects and judge a modification method in consideration of thelife time effect.

3

Particle data group(PDG)

2Chapter 1
Introduction
1.1

Historical introduction

The latter half of the twentieth century saw some quests extended from ordinary atomic systems to those composed of nuclear matter. Most impact
was that the deep inelastic electron collision experiments on protons at MITSLAC indicated that nucleons have an internal structure, they are built of
quarks and gluons.[1] It was the first evidence for quarks as real dynamical constituents and made changes our paradigm of atomic systems. This
paradigm is the quark model, the quark introduced by Gell-Mann in 1964
and the gluon with the idea of color introduced by Nambu and Han and also
by Greenberg in 1965.
The field theory that describes these partons, quarks and gluons, is thequantum chromodynamics(QCD). This theory leads to the conclusion thatsingle free quarks or gluons cannot be studied or observed in our laboratories,
because they are confined by the strong interaction that binds them to eachother.
Another impact in the side of theory at another extreme condition, thatis the high-temperature phase, was that QCD has led to detailed investigations of thermodynamic properties of quarks and gluons, in other words,of deconfined phase ”quark-gluon plasma”, with implemantations of lattice
formulation and the continued exponential increases in computing power.[3]A figure1.1 is a result of lattice QCD simulations with dynamical quarks(Nf 6= 0). Quark masses empolyed in the figure are mu,d /T = 0.4 for Nf = 2,
mu,d,s /T = 0.4 for Nf = 3 and mu,d /T = 0.4, ms /T = 1.0 for Nf = 2 + 1.

1

Figure 1.1: Lattice QCD[3] results for the energy density/T 4 as a functionof the temperature scaled by the critical temperature TC . Note the arrows
on the right side indicating the values for the Stefan.Boltzmann limit.
This large change of energy density at transition temperature are seen in
all three cases. The deviations from ideal gas(the Stefan-Boltzmann) limit
are also seen at high temperature. At the chiral limit(mq = 0), the criticaltemperatures are found to be Tc (Nf = 2) ∼ 175 MeV, Tc (Nf = 3) ∼ 155
MeV. Corresponding critical energy density can be read off from the figure
as ²c ∼ 1GeV f m−3 . The large difference between ²SB /T 4 (Nf ) and ²/T 4 (Nf )at high temperature indicates that the gluons are still interacting above Tc .

2

1.2

High energy heavy ion collision

One of the ways to create QGP is thought to use relativistic nucleus-nucleus
collisions. In the case of nucleus-nucleus collisions with lower energy, provided
at CERN-SPS and BNL-AGS, lower temperature but high baryon density
matter could be achieved. In head on nucleus-nucleus collisions such as√√
Au+Au with sN N = 200GeV , where sN N is center of mass energy per
nucleon pair, a high energy and density matter could be produced, but low
in baryon density.

1.2.1

The picture of heavy ion collisions

In ultra-relativistic heavy ion collisions the de-Broglie wavelength of the individual nucleons is so small that the nuclei can be seen as an independentaccumulation of nucleons. This simplistic view implies that the Lorentzcontracted nuclei interact only in the region of geometrical overlap, determined by the distance between the centers of the two collided nuclei(b), it
is called impact parameter ,see a figure1.2. The corresponding nucleons arecalled participants, while the nucleons outside the geometrical overlap, thespectators, are basically unaffected by the collision. We name the degreeof collisions as the centrality. The most interesting phenomena of a nuclear
matter is in most central collisions.

Figure 1.2: Schematic view of two colliding nuclei in the geometicalparticipant-spectator model[15].
3Figure 1.3: Exaggerated polt of observed rapidity distribution of generated
hadrons in ultra-reativistic nuclei collisions
The participants interact with each other in the reaction zone, leading to
the formation of a hot and dense region, the fireball. There are two basic
scenarios for the formation of the fireball depending on the nuclear stoppingin the reaction. For large stopping, described in the Landau model, thecomplete kinetic energy of the nucleons is converted into thermal energy
and a baryon-rich fireball is formed. The characteristic rapidity distributionof produced particles in such a reaction has a maximum at mid-rapidity.
In the Bjorken-McLerran scenario, the stopping is limited and the nucleons
penetrate each other, they exhibit transparency. This leads to a fireball withlow baryo-chemical potential as the baryon number remains concentrated
near the beam rapidity. The rapidity distribution in this case should be
essentially flat in the rapidity region between the two beams like a figure1.3.
In reality particles in the fragmentation regions and in the central rapidity region are not separated. Their rapidity distribution overlap[7]. In thesimplest terms, we can search the properties of QGP to measure hadrons at
mid rapidity region.

1.2.2

Jets

Jet production was first observed at e+ e− colliders in 1975. The simple
process for producing hadrons is;e+ e− → q q̄
4

(1.1)

At the center mass system, quark and anti-quark(leading partons) becomecharged and neutral hadrons and appear in the form of two oppositely jets.
The hadrons of jets are generated around q q̄-axis because of the potential
between quarks, I mean at lager distance the potential increased indefinitely
generates a quark pair and confine the quarks inside hadrons. High energetic
hadrons appear from jets.
In the case of hadron-hadron collisions, parton-parton scattering can givefour jets in a strict case; one from each of the scattered partons and two beamjets from the spectator partons which carry on along beam directions. As
regards high pT measurements, we give little thought about beam jets. The
signature for a jet is large energy deposition in a localized area of electromagnetic calorimeter.

1.2.3

Nuclear modification factor

I will focus on what is arguably the most important result from the RHIC
program: the observed depletion in the yield of high transverse momentum
hadrons. Nuclear effects on single particle observables are quantifed by the
nuclear modification factor, RAA ; suppression ratio of a particle yield in
Au+Au collisions for it in proton+proton collisions.
Ã

RAA =

! Ã

1 d2 N AA
hNcoll i d2 σ pp/
pp
Nevt dpT dy
σinel
dpT dy!

(1.2)

This quantity is the ratio of the observed per-event yield in nuclear collisions to the expected yield. The latter is the product of the p + p crossd2 σ ppcoll isection, dp, and a scale factor hN, which is explained as fllows. If the Au
pp
σinel
T dy
+ Au collisions were simply a collection of superimposed p + p collisions, thecross section for a given inelastic process would be simply be product of thetotal number of nucleons participating in the collision(Npart ) and the inelastic
pp
nucleon-nucleon cross section (σinel). The cross section for soft production
can reasonably be expected to scale in such a way.

1.2.4

Jet conversion

Initially, energy loss of a leading parton had been attributed to induced gluon
radiation by scattering of the leading jet parton with thermal partons fromthe medium. Perturbative calculations of this process yield results for RAA
5

compatible with data after fixing one parameter characterizing the strength of
the interaction, the transport coefficient q̂ or an equivalent quantity. That isquark and gluon jets are well-defined concepts in a medium. This claim might
have some validity in the case that the mean-free-path of leading parton is of
the order of the size of medium, i.e. L ≤ λ. Energy loss is then dominatedby one gluon radiation.
However the situation is different, generally speaking. When highly energetic partons propagating through dense QCD matter, their fragmentation
pattern changes in the presence of a strongly interaction medium. I meanthat there is the effect not only from thermal properties,like a gluon radiation, but also from chemical properties of medium. In the processes thatjets couple to chemical properties, the flavor of fragments change, for example flavor changing compton processes q + g ↔ g + q , annihilation andpair creation q + q̄ ↔ g + g. Measurements of identified hadrons at high pT
can constrain the rate of flavor conversion. It is naturally that the energetic
partons of fragments become high pT hadrons in final state. So the ratioof identified hadrons at high pT have effective information about the rate offlavor conversion. With sufficient experimental sensitivity this would lead toestimates for the mean free path λ of the jet in the medium, complementary
to measurements of q̂. Such measurements is expected to provide additional
stringent tests for the validity of any model for the jet-medium coupling.
The hadrochemical composition of jet fragments changes significantly inthe presence of parton energy loss. Heavier hadrons become more abundant.
As seen in below figuare, for an Ejet = 50 GeV jet, the kaon to pion ratio
is around 0.4, it is twice of the ratio about the vacuum jet, the proton topion ratio is around 0.5 [4]. These medium-induced changes persist over theentire transverse momentum range. They decrease slightly with increasing
jet energy, but remain clearly visible even for Ejet = 200 GeV jets.
We suggest the relative yield of strange hadrons at high pT as a newsignature for jet medium coupling. The ratio of strange quarks to the sum
up and down quarks,
s
w=
(1.3)
u+d
is about 5 % for the initial leading jet particle at RHIC energies at a typical
pT of about 10 GeV/c. A rough estimate[5], assuming dominabce of compton
channels in the initial hard scattering, would give it, the ratio of strange

6

±

Figure 1.4: Kπ± and p(p̄)
ratios in jets with energies Ejet = 50, 100and200GeV
π±[4].
quarks to the sum of up and down quarks,
wjet (pT = 10GeV ) ∼ wpdf (x ∼ 0.1, Q ∼ 10GeV ) ∼ 6.4%

(1.4)

However, in a chemically equilibrated QGP at given temperature the ratio isw(T ) ∼m2s
K2 (ms /T ).
4T 2

(1.5)

assuming massless up and down quarks. For a strange quark mass of ms =100M eV the ratio is almost half even at Tc ∼ 180M eV :w(Tc ) = 0.47. The
difference between wjet and w is rather large and we have to expect that therelative abundance of strange quark jets will rise with time.
For an infinite medium the particle ratios of jets would equilibrate to thatof the medium. As another case, the same will happen to their momentum
distribution, making them indistinguishable from the medium with a final
7

state measurement. For a finite path length L, the rate of equilibration
should be a good measure of the strength of the coupling to the medium. In
particular, it should give a good estimate of the mean free path λ between
flavor changing scatterings. The approach to equilibrium will be determinedby the ratio λ/L.
Estimation of K 0 S (short-lived neutral K meson) measurement
In this section I discuss the K 0 S measurement at RHIC energy and LHC
energy. It is obvious that the interaction of jet with medium can change theflavor of the jets, defined here as the flavor of leading parton. Nevertheless,most studies of jets in nuclear matter still focus on solely on the kinematicaleffects, based on quenching of longitudinal momentum and broadening oftransverse(right angle against longitudinal direction) momentum of the leading parton. For example, Observable RAA are sensitive to various integrals
over the differential energy loss dE/dx and ultimately measure the momentum transfer per path length, commonly known as q̂. It is summarized as
the effect of jets coupling to the thermal properties of the medium. So it is
so interesting that the look of flavor effect from jets coupling to the chemical
properties of the medium. Measurements of identified hadrons at high transverse momentum(| pT |) constrain the rate of conversions. With sufficientexperiment sensitivity this would lead to estimates for the mean free path λof jet in the medium, complementary to measurements of q̂.
A figure1.5 is the result of theoretical expectation[11] at RHIC energy.
On the right-hand side it is a plot of the RAA of K 0 S as a function of pT .
we observe that conversions greatly enhance the yield of K 0 S in nuclear collisions. In fact, conversions could lead to a RAA that is up to a factor 2larger at high pT than that for pions or protons. A recombination contribution is not included in this study, so caution has to be exercised at lower pT .
This study predicts that the measurement of the RAA of K 0 S at high pT will
provide a unique signal for jet conversions in the QGP fromed at RHIC.
At a figure1.6 we observe that jet conversions have only a small impact on
K0S
RAA at LHC energy. This had to be expected, because initial jet production
is gluon dominated and strange quark jets are not very much suppressed to
begin with, very unlike the situation found at RHIC. The impact of jet
conversions on the RAA of K 0 S is similar to the effect on pions at LHC.
We conclude that strange hadrons might no longer be a good probe of jet
conversions at LHC energy.
8Figure 1.5: K0s spectra from quark and gluon jet fragmentation in p+p√
collisions at sN N = 200GeV [8]. Data are from STAR Collaboration[9].
RAA for K 0 S in Au + Au collisions at same center mass energy as a functionof transverse momentum [11].

Figure 1.6: RAA for K 0 S in P b+P b collisions atof transverse momentum[11].
9√sN N = 5.5T eV as function

Chapter 2
Experimental setup
2.1

The RHIC accelerator

The Relativistic Heavy Ion Collider(RHIC) was proposed in 1990 initiallyand built in the Brookhaven National Laboratory(BNL) in the United Stateof America. Simply stated the RHIC is a colliding-beam accelerator which
has two ring synchrotrons. The RHIC has provided collisions of various ions,that is proton, deutron, Cu and Au, for about ten years. The designed
luminosity is 2 × 1026 cm−2 s−1 for Au + Au and 2 × 1032 cm−2 s−1 for p + p.
The bunch crossing intervals is 106 nsec when there are 120 bunches in eachring.
The RHIC is designed to accelerated protons up to 250 GeV and Au nuclei
up to 100 GeV per nucleon. I state about the Au ion beam, its journey starts
in the Tandem Van de Graaff and accelerated up to 1 MeV per nucleon. The
Tandem Van de Graaff consists of two electrostatic accelerators which iscapable of producing voltage up to 15 million volts, and the ions are injected
into the Booster. The Booster accelerates them up 95 MeV per nucleon.
They are injected into the Alternating Gradient Synchrotron (AGS) andaccelerated to 8.86 GeV. When the ion beam reaches top speed in the AGS,
they are injected into the next beamline called the AGS-To-RHIC (ATR)
transfer line.
The RHIC’s 3.86 km ring has six intersection points where its two rings ofaccelerating magnets cross, allowing the particle beams to collide. At theseintersection points, four current experiments can operate, these are STAR,PHENIX, PHOBOS and BREAMS.

10

Figure 2.1: Schematic view of the RHIC complex[16].
PHENIX, the Pioneering High Energy Nuclear Interaction eXperiment,is the largest of the four experiments. PHENIX is designed specifically tomeasure direct probes of the collisions such as electrons, muons, and photons
by its multi purpose detectors. In the subsequent sections we describe thePHENIX detector and its various detector components.

2.2

The PHENIX detectors

2.2.1

PHENIX complex overview

In the following a short survey of PHENIX experiment[6] will be given. As
the focus of this work is the search for long-lived netural K mesons with
ElectroMagnetic Calorimeter(EMCal), decribing them in more detail in 2.2.4.

11

Figure 2.2: The PHENIX Detector configuration(2007)[17].
122.2.2

Zero Degree Calorimeter(ZDC)

Simply stated the ZDCs consist of two hadron calorimeters located at ±18.25m
from the primary vertex between deflecting dipole magnets of RHIC magnet system. The ZDC design goals are three. First is to provide a common
luminosity measurement for all RHIC experimetns. In fact, the ZDC are
positioned at each offour RHIC experiments. Second is to provide a common
centrality determination with the BBC(below stated). Third is to provide aminimum bias trigger free of beam gas background.

Figure 2.3:
The configuration and the location of Zero Degree
Calorimeter(ZDC)[18].
North and south ZDC is made of alternating tiles of plates of tungsten
and layers of optical fibers. The direction of the plates and layers are tilted
by 45 degree relative to the incident neutron direction. The ZDC is designed
to measure the number of neutron from the collision to collect the Cerenkov
light. A high energy neutrons from the collision generate some perticles,
pions, protons and neutrons etc, to interact with nucleus of the tungsten
absorber. Generated particles make same interactions again and again, we
measure the Cherenkov light from the generated charged particles.

13

2.2.3

Beam Beam Counter(BBC)The BBC is hexagonal quartz Cherenkov radiator installed on about one
and a half meters from the center of PHENIX detector for both North andSouth arm along beam axis. The design purposes of the BBC are five. First
is to provide a collision vertex. Second is to provide a common centrality
determination with the ZDC. Third is to provide a minimum bias trigger.
Fourth is to provide a time-zero determination. Fifth is to provide a reaction
plane determinaion.

Figure 2.4: One element of Beam Beam Counter(BBC)[19].
I said, The BBC element is a quartz Cherenkov raditor. we can measure
a multiplicity of charged particles having β > 0.7 in the forward rapidity
range, here β is a ratio of velocity of charged particle and velocity of light(c).
Each photon-multiplier converts cherenkov light into electrons in order tomeasure it as electrical signals.
The BBC consists of two identical sets of counters installed on both sidesof the collision point along the beam axis. One set is comprised of 64 BBC
elements. The interaction position along the beam axis is calculated fromindividual time measurements of fast leading particles hitting BBC elements
14

Figure 2.5: The location of Beam Beam Counters north and south(BBC)[19].
on the both sides of the interaction point. With an intrinsic timing resolutionof 70 ps, BBC determines the interaction position with a precision of 0.6 cm.

2.2.4

Electro-Magnetic Calorimeter(EMCal)

The EMCal of PHENIX is an electro-magnetic calorimeter at mid rapidity.
The calorimeter measures position, energy and time of flight of incoming
particles. Basically the principles of detection is that electrons and photons interact electromagnetically, bremsstrahlung and pair production, andproduce electromagnetic showers. In the case of hadrons, these particles inthis energy range are typically Minimum Ionizing Particles(MIPs) and deposit only part of their energy in hadronic showers. This EMCal of PHENIX
has two parts, sampling calorimeter(PbSc) and homogeneous, leading-glass
volume cherenkov radiator(PbGl).
Lead Scintillator Calorimeter (PbSc)
The PbSc electromagnetic calorimeter is a sampling calorimeter made ofalternating tiles of Pb ans scintillator consisting of 15552 individual towers
and covering an area of approximately 48m2 . The PbSc module consistsof four towers, each with 66 layers of 0.15 cm lead abosorber and 0.4 cm
scintillator. The layers are optically connected via wavelength-shifting fibers
for light collection by a photon-multiplier. Groups of 6 × 6 modules areconnected mechanically to a self-supporting supermodule, with 3 × 6 PbSc
15

supermodules forming one sector. One mechanical supermodule contains 144
towers and is read out by one Front-End-Module(FEM).

Figure 2.6: (left)Interior view of one PbSc tower, consisting of 66 layers, thisshow only 3 layers (right)Interior view of one PbSc module, consisting of four
towers[20].
The Front-End-Modules differ in detail for various subsystems but theirgeneral layout is similar. They consist of the Front-End-Electronic(FEE),
which digitalizes the analog signals from the detector elements and buffer
the data to wait for trigger decisions.
Lead Glass Calorimeter (PbGl)
The PbGl has two sector and each lead-glass sector consists of 192 supermodules. One supermodule is formed by an array of 6×4 lead-glass modules,
each with a size of 4 × 4times40cm3 and wrapped in reflecting mylar foil andshrink tube. Each lead-glass module is read out via a photon-multiplier.
The lead-glass calorimeter(PbGl) is a cherenkov calorimeter(n = 1.647).
For example, high energetic photons incident on the PbGl interact mainly via
electron-positron pair production and the produced electrons and positrons
subsequently lose their energy by radiating Bremasstrahlung. These photons
can again produce electron and positron pairs, resulting in the formation ofan electromagnetic shower. Of course there are other processes such photo16

Figure 2.7: A PbGl tower and image of one supermodule[20].
electronic effect and Compton scattering. But they play only minor role inthis energy range.
In the case of hadrons, such as pions and protons, form a so-called
hadronic shower. Its charactreistic quantity is the nuclear interaction length,
the distance where most of the hadrons suffer an inelastic interaction andform further hadrons, mostly pions. Charged hadrons are called Minimum
Ionizing Particles(MIPs). Their energy loss is given by the Bethe-Bloch equation. It is constant over a wide energy range leading to the formation ofcharacteristic MIP peak.
cluster Algorithm
The EMCal readout electronics comprisesalmost 25000 readout channels. For
both EMCals 144 individual towers are read out by one single FEM.
An electromagnetic shower usually spreads over more than one tower, alltowers are calibrated by the Cluster Algorithm I state below.
The towers with more than a threshold are selected. For the cluster
merging, the effect of fusion of a ”true” cluster and a ”background” cluster,
selected cluster is defined by assuming that they are all photons, an isolated
cluster is split into two clusters in the way that the number of clusters is equal
to the number of local maximum in the isolated cluster. In the other word,17

Figure 2.8: Image of a cluster.
if more than one local maximum is found, we split this cluster according to
amplitude and positions of the local maximum.
In a simple case that single photon hit in middle of a EMCal tower likea figure2.8, the Ecore , energy of the ”core” towers, is defined as;
Ecore =

core
X

Eimeans ,

i

(2.1)
P

where Eimeans is the measured energy in i-th tower and coreis definedi
as summing of the towers(1st, 2nd, 3rd, 4th, 6th, 7th, 8th and 9th towers)
belonging to the ”core” towers(5th tower). We demand that the ”core” towers
are in the following condition,
Eipred> 0.02,
mean
Eall
mean
Eall
=

all
X

Eimean ,imean
is the sum of measured energy in all towers belonging to thewhere Eall
”peak-area”(1st to 9th), Eipred is the predicted energy using shower profile ini-th tower. The averaged number of towers belonging to the ”core” towers is
4 towers(2nd, 4th, 6th and 8th).
In fact the Ecore contains 91.8 percents energy of total energy on average.
The energy fraction of the Ecore to the total energy depend on the incident

18

angle, position and energy. The dependence is studied by the GEANT simulation tuned by using obtained performance in test beam and corrected in
the data analysis.

2.2.5

Data acquisition system(DAQ)The RHIC provide the high interaction rates of approximately 500kHz inp + p collisions and the large event sizes in high multiplicity Au + Au events
at a rate of a few kHz. However the bunch crossings occur at a frequency of
9.43 MHz. This means events have a minimum timing distance of about 106
nano second[ns]. In PHENIX the timing signal is distributed by the Master
Timing System(MTS) to all FEM’s which participate in the data collection
process.
PHENIX Timing System
The RHIC clock is provided by the Accelerator Control(AC) group. This key
signal is sent via optical serial links to the Master Timing Module(MTM),
the first stage of the PHENIX timing system. The MTM sends a copy of
the RHIC clock to the Granule Timing Modules(GTM’s) and local levelone(LVL1) trigger system. PHENIX detector system is divided into two
sets of elements: granules and partitions. The GTM’s are synchronized by
the MTM. They manage busy signals from DCM’s, relay them to the LVL1
trigger system and provide the RHIC clock and LVL1 trigger accepts to the
granules, it means FEM’s.

19

Figure 2.9: Block diagram of the PHENIX Online System[21].

20Chapter 3
Analysis
3.1

Analysis Method

Figure 3.1: Image of the 2 π 0 decay mode of K 0 S hitting to the EMCal. K 0 S
decay into 2 π 0 and each π 0 decay into 2 γ.

21This basic idea of the identification of short-lived neutral K meson(K 0 S )is rather simple: Basically we can measure only the energy and the positionof FINAL-STATE particles depending on detectors. So we reconstruct theparticles info before decay with final-states’ energy, in the case of neutral π
meson(π 0 ) we reconstruct π 0 s from photon(γ) pairs; 98.8 % of π 0 is going to2 γ. For the identification of the parent-particle we calculate the invariant
mass, a Lorentz invariant value of four-momentum. Therefore the invarinat
mass of π 0 is,
M 2 π0 = 2E1 E2 (1 − cos θγ1 γ2 ),(3.1)

where E1 and E2 are the measured energy of each γ (suppose γ1 and γ2
arbitrarily) and θγ1 γ2 is the opening angle between γ1 and γ2 calculated fromhit positions.
It is known that almost K 0 S decay into π mesons; 69.20 % of K 0 S is goingto π + and π − , 30.69 % of K 0 S is doing to 2 π 0 . Basically we measure themomentum of charged particles with their flight in a strong magnetic field.
hence we can’t measure the momentum of high energetic particles naively.
The measurement of K 0 S via 2 π 0 decay mode is very challenging, because of the lage combinatorial background in the heavy ion collisions. The
combinatorial background of K 0 S via 2 π 0 ,nC4 , is about the square-fold of
the number of clusters(photons) as large as it of π 0 .
First we reconstruct π 0 pair from γs and select π 0 1 and π 0 2 as K 0 S -origin
candidates. I measure the two gamma invariant mass peak from π 0 and I
confine to two gamma invariant mass value with a gaussian fitting.
M 2 π0 1 π0 2 = (E1 + E2 + E3 + E4 )2 − (px 2 + py 2 + pz 2 ),wherepx = √

x1 E1
x2 E2
+√ 2
2
2
2
x1 + y1 + z1
x2 + y 2 2 + z 2 2

+ √

x3 E3
x4 E4
+√ 2
2
2
2
x3 + y3 + z3
x4 + y 4 2 + z 4 2

py = √

y1 E1
y2 E2
+√ 2
2
2
2
x1 + y1 + z1
x2 + y 2 2 + z 2 2

+ √

y3 E3
y4 E4
√
+
x3 2 + y3 2 + z3 2
x4 2 + y 4 2 + z 4 2
22

(3.2)

pz = √

z1 E1
z2 E2
+√ 2
2
2
2
x1 + y1 + z1
x2 + y 2 2 + z 2 2

+ √

z3 E3
z4 E4
+√ 2
2
2
2
x3 + y3 + z3
x4 + y 4 2 + z 4 2(the coordinates of x, y and z are defined in the Appendix).

Figure 3.2: Schematic view of asingle K 0 S event in the real event,here θ12 is the true opening angle
between γ1 and γ2 , and θ34 is thetrue opening angle between γ2 andγ4Figure 3.3: Schematic view of asingle Ks0 event on calculation,
here θ0 12 is the calculated opening
angle between γ1 and γ2 , and θ0 34
is the calculated opening angle between γ2 and γ4With these calculations we can see the K 0 S signals as the peak in thefour-gamma invariant mass distribution. However the mean life time of K 0 S
is realtively long, these signals may change. In reality, K 0 S s’ mean life(τKs0 )is 0.8958 ± 0.005 × 10−10 second [12]. It is so long comparatuvely that thehigh energetic K 0 S (velocity ∼ light speed(c)) can fly according to the his life
time and his momentum. I anticipate that some mass shifts ”only on above
calculattion” will arise as a result of this life time effect (see figure3.2,3.3). In
23

other words, it may change the signal shape and the peak positions. The basic
reason is that we can’t measure the particles flight near the vertex position
until setting new detector. We calculate the invariant mass assuming K 0 s
decay at the vertex position. Hence we miscalculate the opening angles of
π 0 s from K 0 S , the value of π 0 invarinat mass and K 0 S invariant mass looksmaller than each vacuum mass (See figure3.2 and figure3.3).

Figure 3.4: Diagram of the cluster merging and the cluster spliting on acluster algorithm.
In addition, we have to take it into account the multiplicity dependence
as long as dealing with collisions of a high particle multiplicity such as Au√+ Au collisions at sN N = 200 GeV. Since the matrial for this analysis
is photon(γ), so we discuss only the ErectroMagnetic Calorimeter detects
photons at PHENIX. To tell the truth, this multiplcity generates huge background and naturally those backgrounds interfere a cluster algorithm. We
consider two effects, the one is the cluster merging and the other is the cluster
splitting (See figure 3.4). The former is the effect of integration of a ”true”
cluster and a ”background” cluster, here ”true” cluster means a cluster generated by only a photon from K 0 S . Because of high particle multiplicity there
are many clusters generated by another hadrons around a true cluster. Then24

we may measure the energy merged with the deposited energy from anotherhadrons. To put it another way, it is probably true that we may detect larger
energy than the energy deposited only by a signal γ. The latter is the effectof separation of a ”true” cluster. Because of high particle multiplicity we
may measure the energy of another hadrons merged with a piece of a true
cluster. Finally, we may detect smaller energy than the energy deposited
only by a signal γ.
I estimate these effects with the simulation quantitatively. In the next
section, I describe the simulation method and its results in detail.

25

3.2

Single simulations

Simulation method is a effective way to estimate measured results quantitatively with a large statistics. Generally speaking, what they have several
stages results from the fact that there is several stages in heavy-ion collisions.
It is different which processes we reconstruct. Briefly, there are four processes
in the simulation we used. First is the simulation of collisions. The two ion
beams accelerated by RHIC will collide and interact. With enough statistics
the yields of generated particles go along each cross section measured or expected. Second is the simulation of generated particles from vertex, it meansa One’s outputs. Third is the simulation of detector response in particles
flying, it means two’s outputs are three’s inputs. Fourth is the simulation
to change the simulated-data ,third outputs, into the offline Summary Tables(DST). , where the raw data are converted into quantities with more
physical meaning. In this thesis work I simulate second, third and fourth
processes.

3.2.1

Event Generator

We used the one of event generators called as ”EXODUS”[13] based on Monte
Carlo codes. I used it to generate the input single particles. For purposesof this simulation program, an event is viewed as a list of the particles with
their type, energies, momenta, the point of peroduction and the time of
production. We can let off K 0 S having these status as I do. For instance, we
let off K 0 S having full range in order to estimate a geomertrical acceptancefor K 0 S . Then we can’t gain the yield of low pT K 0 S enough, we change theinput particle pT distribution to it enhanced at low pT .
• 4 ≤ pT K 0 S ≤ 14[GeV ], pT distribtion is flat in a figure3.5,• −0.5 ≤ y(rapidity) ≤ 0.5, rapidity distribtion is flat,• 0 ≤ φ < 2π, φ distribution is flat,• Branch ratio of K 0 S to 2 π 0 is 30.69 percents,

26

Figure 3.5: The pT distribution of primary K 0 S .

27

3.2.2Detector Simulation

As you see the figure2.2, the PHENIX detectors are so complex divided their
resposibilities. There are a large of detector types and matrials inside it.
The PHENIX Integrates Simulation Application(PISA) is introduced in order to simulate all response in the PHENIX complex. PISA is the PHENIX
simulation software package based on GEANT libraries [14]. Using PISA,a PHENIX simulator can recognize aspects of the whole PHENIX detectors’ geometry and materals and convert the GEANT particle tracking into
simulated detector signals.
When I measure photon energy with PbSc EMCal, charged π meason is
expected as a huge background. High energetic cahrged particles lose energy
in matter. With respect to PbSc EMCal, there is 66 layers of 0.15 cm leadabosorber. In brief, charged particles go through 9.9 cm lead abosorber at
least. At RHIC energy, most relativistic particles have mean energy loss rates
close to the minimum, and are said to be minimum ioninzing particles(MIPs).
I’ll take the case of − dE
= 2[M eV g −1 cm2 ][12], charged π meason lose energydx
about 225 MeV. To tell the truth, charged particles do not go straight in thelead due to multi-scattering. I use clusters having more than 300 MeV energy
as hard cut in order to rid all cluster of clusters from charged π mesons.

Figure 3.6: Invariant mass spectrum of single K 0 S events for highpT with a gaussian fitting.

Figure 3.7: Invariant mass spectrum of single K 0 S events for highpT with a landau fitting.

As you see the figure3.6, Once I use the gaussian as a fitting function,a distribution of 4 photons invariant mass looks asymmetry due to the life
time effect.
28

Then, I try to fit this four photons invariant mass distribution with themodified landau function (See the figure3.7). Here,x−C
x−C− exp()],
BB
1−(x − E)2
gaussian function ≡ g(x) ≡ √ exp(
),
2D2
D 2π

landau function ≡ f (x) ≡ A × exp[

(3.3)
(3.4)

where A, B, C, D and E are the fitting parameters. I define that B isa width and C is the most probable value for landau function, D is a widthand E is mean value for gaussian function.

0

Figure 3.8: four gamma invariant mass distribution in 4.5GeV ≤ pT K S ≤5GeV with a gaussian fit.

0

Figure 3.9: four photons invariant mass distribution in 11.5GeV ≤ pT K S ≤12GeV with a gaussian fit.
I show the figure3.8 and the figure3.9. I separate the four photons invariant mass spectra according to four photons pT , one pT bin range is 0.5GeV,
29

than one bin in the figure3.6, 10 GeV ≤ pT ≤ 14 GeV. I fit these distributions
with a gaussian and a linear function. There is a enhaced counts around 0.5
GeV in the figure3.9 and the figure3.8 don’t look so.
Here, we have to take into consideration that the K 0 S life time is relatively
long and we can’t measure the track very near collision vertex. As I stated thelife time effect in the previous section, this effect lead to like a lower mass shift
in invarant mass distribution. In this respect, it is expected that the mass
peak is changing according to the K 0 S pT . So there are flater distribution in
the wide pT range like the figure3.6. I suggest a way to modify this effect innext section.

3.2.3

Comparison between the landau fitting and gaussian fitting for 4 photons invariant mass distribution

I stated that the langau fitting looks fine more than the gaussian fitting for 4
photons invariantmass distribution. I show the results of the comparison between the landau fitting and gaussian fitting in the figure3.10, the figure3.11
and the figure3.12. There is easily no comparison between gaussian mass
peak and landau peak due to these function characteristics. Gaussian peakmeans a mean of invariant mass value of a peak, meanwhile landau peakmeans a most probable invariant mass value of a peak. In a figure??, for all
pT range(7-14 GeV) landau peak values are larger than gaussian peak values
and both values are smaller than a vacuum mass of K 0 S ; 0.498 GeV.
In a figure3.12 for all pT range landau fitting converted χ2 s are smaller
than gaussian fitting converted χ2 s. It means a landau fitting looks fine morethan a gaussian fitting. So I use a landau fittig for 4 photons invariant mass
distribution.

30

Figure 3.10: Peak position of the K 0 S as a function of the pT with the landau
and gaussian fitting.

Figure 3.11: Peak width of the K 0 S as a function of the pT with the landau
and gaussian fitting.

31

Figure 3.12: Chi square of the landau and gaussian fitting about the mass
peak of the K 0 S .

32

3.2.4

Estimation of the Decay Vertex Location

Figure 3.13: Image of Decay Vertex Location(DVL).
In the previous section, we stated the life time effect. It is difficult tomeasure each K 0 S lifetime, it is possible to reconstruct a K 0 S and measureeach K 0 S momentum with the EMCal. In addition it is known that the mean
life time of K 0 S is 0.8953 × 10−10 second.
I fix that all K 0 S life time is the mean life time. Then I calculate the mostprobable Decay Vertex Location(DVL). The mean life time is the time until
a K 0 S decay in the K 0 S rest frame. High energetic K 0 S travels at almost the
speed of light. For an observer on the earth(labratory system) the rapidly
moving reference frame of K 0 S s elapse more slowly, the K 0 S mean life timeis lengthened to γ τK 0 S .

DV Lx,y,z [m] = vK 0 S × γ × τK 0 S

P K 0 S~x,y,z c~ 0S | c
| PK

0
~ 0S
PK
PK Sc
EK 0 Sx,y,z c× τK 0 S=×c×2
0~ S |c
EK 0 SMK 0 S c| PK
c × τK 0 S=
× cP K 0~S x,y,z
M K 0 S c2

33

(3.5)
(3.6)
(3.7)

∼ 0.053941408 × cP K 0~S x,y,z(3.8)

where c is the speed of light [m/s], τK 0 S is 0.8953 × 10−10 [s], MK 0 S c2 is~ 0 S | c is a calculated probablely momentum [GeV]
0.497614 [GeV ] and | P K
of a reconstructed K 0 S . For instance, a calculated probablely momentum is
14 GeV, then K 0 S is alive for 0.76 m from a collision vertex.
I recalculte the vectors of clusters from the DVL. Naively this recalculation is expected to modify the π 0 opening angle, the calculated invarinat
mass of π 0 and the calculated invariant mass of K 0 S .
The comparison between the DVL analysis and the normal analysis
I report the comparison between the Decay vertex location(DVL) analysis
and the ”normal” analysis here. The main difference between the former andthe latter is whether I recalculate the invariant mass of four photons withthe most probable decay vertex location or not.

Figure 3.14: Invariant mass peakof 2 photons with gaussian fitting.
The red line is to take into accountthe DVL. The green line is not totake into account the DVL.

Figure 3.15: The width of the 2
photons invariant mass with gaussian fitting. The red line is to take
into account the DVL. The green
line is not to take into account the
DVL.

I fit the constant in a figure3.14 and a figure3.15 to get cut-values when I
calculate the four photons invariant mass and to reduce backgrounds. These
results are shown in a table3.1;

34

Table 3.1: The results of the fitting of the peak position and the width intwo photons invariant mass distribution.
most probable mass value [GeV] width of the mass peak [GeV]
DVL results
0.127073
0.0113321
Single results
0.126865
0.0114572

Figure 3.16: Peak of the 4 photons invariant mass with landau fitting. The
red line is to take into account the DVL. The green line is not to take into
account the DVL.
A figure3.16 show a most probable invariant mass value of K 0 S meason
with DVL and without DVL. Each result is separated by color, red plotmeans DVL results and green plot means normal results, out of considerationof DVL. A figure3.17 show a width of landau fitting in 4 photons invariant
mass with DVL and without DVL. A figure3.18 show a χ2 of each landau
fitting.

35

Figure 3.17: Width of the 4 photons invariant mass with landau fitting. The
red line is to take into account the DVL. The green line is not to take into
account the DVL.

Figure 3.18: χ2 of a landau fitting. The red line is to take into account the
DVL. The green line is not to take into account the DVL.

36

3.3

Embedding simulation

In the previous section, we stated the mulitiplicity effect. We explain how wetake account of the multiplcity effect in this section. We use the techniquecalled ”embedding simulation”; embedding of the simulated particles into
real event. The main flow of the embedding simulation is described in thefollowing.
For this embedding, a DST(Data Summary Table) containing real data(taken
at 2004)is read in together with a few simulated DSTs for single K 0 s . The
simulated events are scaned into devided vertex classes by a z-vertex location
and real events are only considered if they satisfy the same collision vertex
class. For each selected real event the EMCal tower information, depositedenergy, is extracted from the DST and merged with the tower informationfrom one simulated event. The list of merged towers is the basis for a newcluster. For the above-mentioned reason, the result list of merged clusters isdifferent from the list of clusters from the real event. A comparison yields
the modified or new clusters in the merged event and the lost clusters fromthe real event (See Figure3.19).
The embedding output contains also data copied from the real and thesimulated DST into new merged DST. This new DST have information suchas trigger data of real events and ancerstry information of single K 0 s simulation. To sum up, the embedding output have ;• Such as centrality and vertex, event information from the real event• Lists of EMCal clusters containing the new hits after embedding,• Lists of EMCal clusters from the pure single K 0 s simulation,• Simulated particle information, such as parent particles, primary momentum and energy.
I calculate the invariant mass of two photons with this embeded simulation data using the formula3.1. It can be seen that π 0 mesons from K 0 S
mesons merging to the background.
Energy Asymmetry of cluster pair In contrast to single simulation,
there is a huge combinatorial background in embeded simulation. One possibility to reduce background is to apply the energy asymmetry limit; definedas37

Figure 3.19: Main flow of the embedding algorithm[15].
38α=| E1 − E2 |E1 + E2(3.9)

where E1 and E2 is each measured energy. Since a photon pair from π 0
is massless and perfectly symmetric in the π 0 rest frame, a energy asymmetry value is expected 0 in the π 0 rest frame. In the lab system a energy
asymmetry distribution from π 0 is flat. On the other hand, a energy ofmost background is expected relatively low because it is known genericallya energy of background has exponential distribution. As a result, a energy
asymmetry of background is expected as strongly peaked around 1
2 photons invariant mass spectra After fitting a gaussian function, we
get mean and width of a invariant mass of two photons in each centrality
bin from these figures like as a figure3.20, a figure3.21, a figure3.22 and afigure3.23. The more it is a central collision, the more the nunmber of generated particles increases. There are larger background in the most central
collisions and in minimum bias than in the peripheral collisions. Then, I use
a harder energy asymmetry cut, less than 0.7, in order to reduce a combinatiorial background in the most central and in minimum bias. Here, ”0-30
percents centrality”, ”30-60 percents centrality ”, ”60-92 percents centrality”
and ”Minimum Bias” mean the high multiplicity, the mid multiplicity, thelow multiplcity and no selection of multiplicity respectively in a figure3.23,
a figure3.22, a figure3.21 and a figure3.20.

The comparison between embeded simulation and single simulation
for the invariant mass distribution of 2 photons
At first I show the embeded and single results of the invariant mass distribution of 2 photons from K 0 S in a figure3.24, a figure3.25 and a figure3.26.
As a figure3.24, for all pT range(4-11 GeV), gaussian peak values of embeded
simulation are larger than gussian peak values of single simulation. There is
no gap of width values between embeded simulation and single simulation ina figure3.25.

39

Figure 3.20: The invariant mass of
two photons in the range of two
photons pT from 8GeV to 8.5GeV
at the Minimum Bias.

Figure 3.21: The invariant mass of
two photons in the range of two
photons pT from 8GeV to 8.5GeV
at the peripheral collisions.

Figure 3.22: The invariant mass of
two photons in the range of two
photons pT from 8GeV to 8.5GeV
at the mid central collisions.

Figure 3.23: The invariant mass of
two photons in the range of two
photons pT from 8GeV to 8.5GeV
at the most central collisions.

Figure 3.24: Peak position of the π 0 for the comparison between a Embedding
simulation and a Single simulation.

40

Figure 3.25: Peak width of the π 0 for the comparison between a Embedding
simulation and a Single simulation.

Figure 3.26: Chi square of the gaussian fitting about the mass peak of the π 0
for the comparison between a Embedding simulation and a Single simulation.

41

Table 3.2: The results of the fitting of the peak position and the width intwo photons invariant mass distribution.
mean mass value [GeV] width of the mass peak [GeV]MB
0.129417
0.0120298
0-30 % central
0.129995
0.0120902
30-60 % central
0.129198
0.0108887
60-92 % central
0.127644
0.0117368
Single simulation
0.12676
0.00949414
Secondly, I show the embeded and single results of the invariant mass
distribution of 2 photons from K 0 S for each mulitiplcity.

Figure 3.27: Peak position of the π 0 for the comparison between a Embedding
simulation and a Single simulation.
I fit the constant in a figure3.27 and a figure3.28 to get cut-values when I
calculate the four photons invariant mass and to reduce backgrounds. These
results are the table3.2;42Figure 3.28: Peak width of the π 0 for the comparison between a Embedding
simulation and a Single simulation.

Figure 3.29: Chi square of the gaussian fitting about the mass peak of the π 0
for the comparison between a Embedding simulation and a Single simulation.

43

The comparison between embeded simulation and single simulation
for the invariant mass distribution of 4 photons
With a π 0 mass range of the previous section, I show results of 4 photons
invariant mass for each centrality and single simulation in a figure3.30, afigure3.31 and a figure3.32.

Figure 3.30: Peak position of the K 0 S for the comparison between a Embedding simulation and a Single simulation.

44

Figure 3.31: Peak width of the K 0 S for the comparison between a Embedding
simulation and a Single simulation.

Figure 3.32: Chi square of the gaussian fitting about the mass peak of theK 0 S for the comparison between a Embedding simulation and a Single simulation.

45

Chapter 4
Results and Discussion
Here, we show the results of ratios in order to lead to a conclusion. I statea effectivity of a DVL method first. Next, I show multiplcity effect of eachcentrality for a K 0 S measurement. A outlook for the further analysis isdiscussed in the end.

4.1

Comparison between DVL analysis andnormal analysis

4.1.1

Results of DVL analysis for π 0 s from K 0 S

Figure4.1 and figure4.2 show mean values of 2 photons mass peak and widthsof it as a transverse momentum function. DVL results agree in single simulation results within the margin of statistical error in a figure4.1 and figure4.2.

46

Figure 4.1: A ratio of π 0 peak from K 0 S between DVL analysis and normal
analysis as a 2 photons transverse momemtum(pT ).

Figure 4.2: A ratio of π 0 width from K 0 S between DVL analysis and normal
analysis as a 2 photons transverse momemtum(pT ).

47

4.1.2

Results of DVL analysis for K 0 S

Figure 4.3: A ratio of K 0 S peak between DVL analysis and normal analysis
as a 4 photons transverse momemtum(pT ).
Figure4.3 and figure4.4 show mean values of 4 photons mass peak andwidths of it as a transverse momentum function. DVL results agree in single
simulation results within the margin of statistical error in a figure4.3 andfigure4.4. We can’t see a expected fine tune with DVL calculation even athigh pT range.

48

Figure 4.4: A ratio of K 0 S peak between DVL analysis and normal analysis
as a 4 photons transverse momemtum(pT ).

49

4.2

Multiplicity effects

4.2.1

The results of the multiplicity effects for π 0 s from
K 0S

I show the ratio of π 0 s’ peak-values and widths in order to investigate themulitiplicity dependence in the figure4.5 and the figure4.6.

Figure 4.5: Ratio of postion of π 0 peak between embedding simulation andsingle simulation as a function of 2 photons pT for each centrality.
In these figures, the red plots mean the selection of the minimum bias
events. Furthermore, the green plots mean the selection of 60-92 % central
events, the blue plots mean the selection of 30-60 /the magenta plots mean
the selection of 0-30 % central events. The mean mass values of embedding
simulation are basically larger than the man values of single simulation.

50

Figure 4.6: Ratio of Width of π 0 mass between embedding simulation andsingle simulation as a function of 2 photons pT for each centrality.

51

4.2.2

The results of the multiplicity effects for the K 0 S
measurement

Figure 4.7: Ratio of postion of K 0 S peak between embedding simulation andsingle simulation as a function of 4 photons pT for each centrality.
I show a ratio of invariant mass peak values in a figure4.7, a ratio ofinvariant mass width in a figure4.8. Most probable mass values of embeded
simulation of each centrality agree in them of single simulation within themargin of statistical error.

52

Figure 4.8: Ratio of width of K 0 S peak between embedding simulation andsingle simulation as a function of 4 photons pT for each centrality.

53

Figure 4.9: On going PHENIX integrated luminosity as a function of weeks
into this-year-run[23].

4.3

OutlookI start to analyze the this year data. I show the result of ”on going” PHENIX
integrated luminosity in the figure4.9. The RHIC plans a 10-weeks physics
run in 2010. If we will have been just taking munimum bias data at 5 kHz
flat, we would have recorded around 7.5 billion events, it is about 1.6 times
the Run-7 statistics.

54

Chapter 5
Conclusion
We report the simulation study of signal from K 0 S meson with photonic decay
mode. We measured 2 photons invariant mass distribution of π 0 from K 0 S ,and 4 photons invariant mass distribution of K 0 S in high pT range. In a single
simulation, I discuss peak shape of 4 photon invariant mass and tried to show
effectivity of the new method taking account of estimation of most probabledecay vertex location(DVL). In this study, there is agreement between DVL
results and normal results within the margin of statistical error. I show
multiplicity effects with simulation data and data of the Au + Au collisions√
at sN N = 200 GeV at PHENIX experiment and the effective invariant mass
range of π 0 from K 0 S and K 0 S for each multiplcity as a function of eachparticle’s pT . There is gap about 20 MeV between most probable invariant
mass value of measured K 0 S and vacuum K 0 S mass value. At high pT , peak
distribution of 4 photons invariant mass for each centrality agrees in it ofsingle simulation. Most statistics of Au + Au collisions are expected to betaken in 2010 and there is no reason not to analyze them.

55

Acknowledgement
I would like to express my gratitude to Associate Prof. Kenta Shigaki who
mainly supervise this work. Also, he gave me a great chance to talk to othercollege students and Gabor David, who is one of the foremost researchers in
the PHENIX photon analysis group. Prof. Sugitate, the boss of our laboratory gave me many chances to go to the Brookhaven National Laboratory
and international conferences. I could learn not only the expert knowledgeof detectors but also the physics knowledge. Those experiences had been
good educations and strongly helped to elevate my motivation. AssistantProf. Kensuke Homma gave me crucial suggestions a lot. I would like tothank Yoshihide Nakamiya, Misaki Ouchida and Kotaro Kijima for giving me
precious advice and teaching some computing techniques. I wish to thank
PHENIX collaboration. I’m obilged to Dr. Kyouichiro Ozawa, KEK andphysics office helpers for all their help of business trip. I’m grateful to mycolleages, Iwasaki Takashi, Ueki Yusuke, Chuman Fumihiro and Hiei Ayako.
Finally, I express my gratitude to my spouse Nihashi Yachiyo.

56

Appendix A
PHENIX Coordinate System
The Z axis of the PHENIX coordinate system is defined as a direction of thebeam line. The direction from the vertex point to north Muon Arm is defined
as positive. The X and Y axis are defined as west direction and the vertical.
The direction from the vertex point to the west Central Arm is defined as
positive. The direction from the vertex point to the upward tendency isdefined as positive. The angle φ is defined in X-Y plane as follows at (x, y,z);yx
The angle θ is defined in Y-Z plane as follows at (x, y, z);
φ ≡ tan−1

(5.1)

y
(5.2)
z
The direction of particle is determined with φ and θ. In the high energy
reaction, y is often used. y is called rapidity and is defined as floows;θ ≡ tan−1y≡1
E + pzlog
2
E − pz(5.3)

where E is the energy of particle and pz is the momentum of z-component.
In the case the particle energy is large, the mass of particle is neglible. In
this case,y =1 + pz /E
1log
2
1 − pz /E

57

(5.4)

1
1 + cos θlog
2
1 − cos θ1
cos2 θ/2=log
2
sin2 θ/2θ= − log tan
2

=

(5.5)
(5.6)
(5.7)
(5.8)

The pseudo-rapidity is defined as;
θ
(5.9)
2
The rapidity y can be approximated with pseudo-rapidity η when E isenough large.
η ≡ − log tan

58

Figure 5.1: The PHENIX coordinate system[17].

59Appendix B
landau function
The landau function is defined here as ;landau function ≡ f (x) ≡ A × exp[

x−C
x−C
− exp()],
B
B(5.10)

As you see this function,f (x = C − 5B)
f (x = C − 4B)
f (x = C − 3B)
f (x = C − 2B)
f (x = C − B)f (x = C + B)
f (x = C + 2B)

∼
∼
∼
∼
∼
∼
∼

0.018 × f (x = C)
0.048 × f (x = C)
0.13 × f (x = C)
0.32 × f (x = C)
0.69 × f (x = C)
0.49 × f (x = C)
0.012 × f (x = C)

Then, I integrate the landau function,
Z E
D

A × exp[

x−C
x−C− exp()]dx
B
B(5.11)

I can’t integrate this function mathmatically, I made a computer to calculate them. Here, I set that A is 6000, B is 0.046 and C is 0.47.

60

Figure 5.2: landau distribution.

DC − 5BC − 4BC − 3BC − 2B
C −B
C − 5BC − 4BC − 3BC − 2B
C −B
C − 5BC − 4BC − 3BC − 2B
C −B

E
C + 3BC + 3BC + 3BC + 3BC + 3BC + 2BC + 2BC + 2BC + 2BC + 2B
C +B
C +B
C +B
C +B
C +B

Figure 5.3: landau distribution
with log scale.
RE
A×exp[ x−C−exp( x−C
)]dx
B
B
RD+∞
dx
x−C
x−C
−∞

61

A×exp[

B

−exp(

0.994
0.982
0.953
0.875
0.694
0.993
0.982
0.952
0.875
0.694
0.929
0.918
0.888
0.811
0.630

B

)]

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62

[15] Christian Klein-Bösing Ph. D. Thesis at University of Muenster, 2005[16] Yoshihiro Iwanaga Master Thesis at University of Hiroshima, 2009[17] PHENIX Official Website: http://www.phenix.bnl.gov/WWW/run/drawing/[18] Michey Chiu Talk in the PHENIX Forcus 2004[19] Yuji Tsuchimoto Talk in the PHENIX Forcus 2004[20] Peter Tarjan Talk in the PHENIX Forcus 2004[21] Martin Purschke Talk in the PHENIX Forcus 2004[22] Experimental Quark Physics Laboratory
http://www.hepl.hiroshima-u.ac.jp

OfficalWeb[23] Jamies L. Nagile Report of Run10 in phenix collaboration list63

site: